Question

which of the following are true?
select all that apply.
a. \\(x = 6\\)
b. \\(x = 30\\)
c. \\(m\angle rdt = 77^\circ\\)
d. \\(m\angle adr = 29^\circ\\)
e. \\(x = 4\\)

Explanation:

Identify the relationship between the angles

Using the Angle Measurement knowledge point
The double arc markings on \(\angle ADR\) and \(\angle RDT\) indicate that these two angles are congruent.

$$ m\angle ADR = m\angle RDT $$

Set up the algebraic equation

Using the Angle Measurement knowledge point

$$ 2x + 17 = 3x - 13 $$

Solve for x

Using the Angle Measurement knowledge point

$$
LATEXBLOCK0
$$

Calculate the angle measures

Using the Angle Measurement knowledge point

$$
LATEXBLOCK1
$$

Evaluate the given options

Using the Angle Measurement knowledge point

• Option A: \(x = 6\) (False)
• Option B: \(x = 30\) (True)
• Option C: \(m\angle RDT = 77^\circ\) (True)
• Option D: \(m\angle ADR = 29^\circ\) (False, it is \(77^\circ\))
• Option E: \(x = 4\) (False)

Answer:

• (A) \(x = 6\)
• (B) \(x = 30\) (Correct answer)
• (C) \(m\angle RDT = 77^\circ\) (Correct answer)
• (D) \(m\angle ADR = 29^\circ\)
• (E) \(x = 4\)